Question

Find the value of y. Round to the nearest tenths place.

Answer 1

Are there any options on the test or homework

Answer 2

Answer:

y = 12

Step-by-step explanation:

Look at the left triangle first.  Opposite the 30 degree angle (not shown) is the shortest side, which (according to the sine function) is half the hypotenuse, or 2√3.  Then (2√3)² + x² = (4√3)², or

4(3) + x² = 16(3).  Thus, x² = 16(3) - 4(3) = 12(3) = 36, and so x = 6.  Again using the sine function, we find that x = 2y = 6, so, using the sine function, we find that sin 30° = 6/y.  Thus y = 6 / (2/1) = 12  =  y